Maybe someone with more specialized knowledge can shime in, but this looks awfully similar to me to a discretized SU(1) symmetry (maybe SU(2)? My intuition in Lie algebras is extremely rusty)
If so, hexaflexagons (or general flexagons) could present interesting analogies to Calabi-Yau manifolds, especially in terms of holonomic properties, which might yield some insights or parallels for type II string theory. Or in more intuitive terms as I see it, a flexagon looks suspiciously similar to a string oscillating on a folded dimension, but discretized as some sort of torus/state machine. (not a physicist, worked at a HEP lab ages ago, I hope some of my comment made sense)
If so, hexaflexagons (or general flexagons) could present interesting analogies to Calabi-Yau manifolds, especially in terms of holonomic properties, which might yield some insights or parallels for type II string theory. Or in more intuitive terms as I see it, a flexagon looks suspiciously similar to a string oscillating on a folded dimension, but discretized as some sort of torus/state machine. (not a physicist, worked at a HEP lab ages ago, I hope some of my comment made sense)